Managing personal Outlook.com account settings, security, and privacy
Hey there, N AUD
From what you have posted, it sounds as though the hackers have compromised your account and changed your account alias. Attackers do this because they know it makes it harder for you to get your account back. This is due to the account recovery form returning an error informing you that the Microsoft account no longer exists.
On top of this, they will replace your security information with theirs, making it harder for you to recovery the account.
As you use this account for Xbox, please can you complete the Xbox account recovery form here: https://aka.ms/recovermyaccount
Please include as much information as possible, including your device ID either for your Xbox console. To help find your device ID, please refer to this article here: https://support.xbox.com/en-GB/help/hardware-network/warranty-service/find-xbox-one-kinect-serial-number
Please note that the Xbox/Microsoft account team will contact you via email. Please respond to their email to continue talking to the team. It is worth noting that sometimes account recovery can be unsuccessful, and may lead to Microsoft suspending the account to protect you. This depends on what the attacker has done with your account and if they can recover the Microsoft/Xbox account.
Hope this information helps,
Nathan